In this letter, we will focus on SM extensions by new heavy neutral gauge bosons (\(Z^\prime \) ) which are very popular NP solutions of the \(b\rightarrow s\ell ^+\ell ^-\)  anomalies [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}, [39]}, [40]}, [41]}, [42]}, [43]}, [44]}, [45]}, [46]}, [47]}, [48]}, [49]}, [50]}, [51]}, [52]}, [53]}. While the \(Z^\prime \)  at tree-level preferably gives LFUV effects in \(b\rightarrow s\ell ^+\ell ^-\) , LFU effects can be generated via \(Z-Z^\prime \)  mixing. In fact, because both bosons have the same quantum numbers, this mixing cannot be avoided by any symmetry. Furthermore, in the case that electroweak (EW) symmetry breaking and the breaking of the symmetry giving rise to the \(Z^\prime \)  mass are connected, one even expects a mixing of the order of \(m_Z^2/m_{Z^\prime }^2\) . Importantly, \(Z-Z^\prime \)  mixing has also an impact on the global EW fit, in particular on \(Z\ell ^+\ell ^-\)  and \(Z\nu \nu \)  couplings and if the \(Z^\prime \)  is an \(SU(2)_L\)  singlet (i.e. not the neutral component of an \(SU(2)_L\)  multiplet), also the prediction of the \(W\)  mass is altered compared to the SM. The latter is very important since the current global EW fit displays a tension of \(1.8\,\sigma \)  [54]} and, as we will see, the effect of \(Z-Z^\prime \)  mixing has the right sign to account for this.
